Use of Lanczos Tau Method to Derive Polynomial Approximate from the Addition Theorem of Slater Type Orbitals

Internet Electronic Conference of Molecular Design 2003, November 23 – December 6 Abstract Motivation. Multi-center integrals are certainly the building blocks of quantum chemistry packages ranging from semi-empirical to the so-called ab-initio. The efficiency (accuracy and speed) of the numerical methods used for the computation of such integrals is therefore of extreme importance since millions of these need to be computed for molecules of practical interest. In this work, the Lanczos τ method is applied to derive a polynomial approximate to the so-called one-center expansion of Slater Type Orbitals (STOs). The procedure is applied to the three-center nuclear attraction integrals, which are essential not only in quantum chemistry but also to model electron-molecule scattering. Method. Starting with a spherical Slater Type Orbital a differential equation governing such functions is elaborated. The application of the Lanczos τ to the differential equation enables us to obtain a polynomial approximate, and more importantly the corresponding absolute error. Such an approximate is afterwards used in the master formula allowing the computation of multi-center integrals over STOs. Results. Numerical values for three-center nuclear attraction integrals are reported. Comparison with previous work is performed. Conclusions. Multi-center integrals over STOs are still a challenging problem. The case of nuclear attraction integral is among the problems that can be tackled with various approaches including the one presented in this work. However for fully functional quantum chemistry software using STOs to be efficient it is necessary to combine the best of all methods by selecting the most appropriate tool for each case.